by a Hückel system. The plus-minus orientation of each orbital is arbitrary since these are just basis set orbitals and do not correspond to any molecular orbital. If any orbital were to change signs, two plus-minus overlaps are either removed or added and the parity (evenness or oddness) is not changed. One choice of signs leads to zero plus-minus overlaps for the Hückel array on the right. The butadiene to cyclobutene example Figure 4 shows the orbital array involved in the butadiene to cyclobutene interconversion. It is seen that there are four orbitals in this cyclic array. Thus in the interconversion reactions orbitals 1 and 4 overlap either in a conrotatory or a disrotatory fashion. Also, it is seen that the conrotation involves one plus-minus overlap as drawn while the disrotation involves zero plus-minus overlaps as drawn. Thus the conrotation uses a Möbius array while the disrotation uses a Hückel array. But it is important to note, as described for the generalized orbital array in Figure 3, that the assignment of the basis-set p-orbitals is arbitrary. Were one p-orbital in either reaction mode to be written upside-down, this would change the number of sign inversions by two and not change the evenness or oddness of the orbital array. With a conrotation giving a Möbius system, with butadiene's four electrons, we find an "allowed" reaction model. With disrotation giving a Hückel system, with the four electrons, we find a "forbidden" reaction model. Although in these two examples symmetry is present, symmetry is not required or involved in determination of reaction allowedness versus forbiddenness. Hence a very large number of organic reactions can be understood. Even where symmetry is present, the Möbius–Hückel analysis proves simple to employ. MO degeneracies leading to correlation diagrams It has been noted that for every degeneracy along a reaction coordinate there is a molecular orbital crossing. Thus for the butadiene to cyclobutene conversion, the two Möbius (here conrotatory) and Hückel (here disrotatory) modes are shown in Figure 5. The starting MOs are depicted in the center of the correlation diagram with blue correlation lines connecting MOs. It is seen that for the Möbius mode the four electrons in MOs 1 and 2 end in the bonding MOs (i.e. σ and π) of cyclobutene. In contrast, for the Hückel mode, there is a degeneracy and thus an MO crossing leading to two electrons (drawn in red) are headed